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Year 12 Further Maths Summer Homework
Constant Acceleration Formulae
AKA: Kinematics
Using your knowledge form Additional Maths or by researching on the internet:
fill in the Kinematics Summary Page
Choose from either
Basic SUVAT Questions or
Harder SUVAT Questions
Answer the questions as well as you can showing all your working out and what equations you have used. Your working out needs to be clearly understood by someone who has not read the question.
For more help and a much deeper understanding than just remembering the equations go to:
HYPERLINK "http://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic_formulas" www.khanacademy.org/science/physics/one-dimensional-motion/kinematic_formulas
P.S. Always Draw a DiagramKinematics Summary
Velocity-time graphs
The area under the velocity-time graph is the
The gradient of the velocity-time graph is the
SUVAT Equations
LetterWhat it stands forUnitss
u
v
a
t
The five equations:
1
2
3
4
5
Vertical Motion:
The symbol g is used for
The approximate value of g that we use in M1 is
The direction g acts in is
Basic SUVAT Questions
A particle is accelerated uniformly from rest, so that after 10 seconds it has achieved a speed of 15 m/s. Find its acceleration and the distance it has covered?
A car accelerates uniformly from rest and after 12 seconds has covered 40m. What are its acceleration and its final velocity?
A train is uniformly retarded from 35m/s to 21m/s over a distance of 350m. Calculate the retardation and the time taken to come to rest from the 35m/s.
A particle is accelerated from 1m/s to 5m/s over a distance of 15m. Find the acceleration and the time taken.
A car accelerates uniformly from 5m/s to 15m/s taking 7.5 seconds. How far did it travel during this period.
A particle moves with uniform acceleration 0.5m/s2 in a horizontal line ABC. The speed of the particle at C is 80m/s and the times taken from A to B and from B to C are 40 and 30 seconds respectively. Calculate
(a) Speed at A
(b) Distance BC
Initial velocity 5m/s, final velocity 36km/hr, acceleration 1.25m/s/s. Distance?
A car accelerates from rest with acceleration 0.8m/s2 for 5 seconds. Find the final velocity
A train starts from rest and accelerates uniformly at 1.5m/s2 until it attains a speed of 30m/s. Find the time taken and the distance travelled.
A train travels along a straight piece of track between 2 stations A and B. The train starts from rest at A and accelerates at 1.25m/s2 until it reaches a speed of 20m/s. It then travels at this speed for a distance of 1560m and then decelerates at 2m/s2 to come to rest at B. Find
(a) Distance from A to B
(b) Total time taken for the journey
(c) Average speed for the journey
A car is being driven along a road at 25m/s when the driver suddenly notices that there is a fallen tree blocking the road 65m ahead. The driver immediately applies the brakes giving the car a constant retardation of 5m/s2. How far in front of the tree does the car come to rest?
In travelling the 70cm along a rifle barrel, a bullet uniformly accelerates from rest to a velocity of 210m/s. Find the acceleration involved and the time taken for which the bullet is in the barrel.
Harder SUVAT Questions
Look out for:
Needing to use of motion-time graphs
Necessity of simultaneous equations
Using (t 1) for delayed motion
1. A train stops at two stations A and B. It accelerates from rest from station A to a speed of 144 kmh-1 in 3 minutes and maintains this speed for 10 minutes. It then decelerates for 2 minutes and comes to rest at station B. Find the total distance between A and B.
2. A girl standing on a bridge throws a stone vertically upwards at 6 ms-1. It hits the water below the bridge after 2 seconds. Find the speed at which the stone hits the water and the initial height of the stone.
3. A particle moving in a straight line with a constant acceleration covers 10 m in 2 seconds and 22 m in a further 2 seconds. How much further does it travel in the next two seconds?
4. A train is brought to rest with uniform deceleration. It travels 30 m in the first 2 seconds, and a further 30 m in the next 4 seconds. Find
(i) the initial velocity,
(ii) the deceleration,
(iii) total time to come to rest.
5. A particle accelerates from rest with an acceleration of 3 ms-2 to a speed V. It continues at this speed for time T and then decelerates to rest at 1.5 ms-2. The total time for the motion is 1 minute, and the total distance travelled is 1 km. Find a value for V. (Hint: use a v-t graph to help, and be systematic.)
6. A ball is thrown vertically upwards at 25 ms-1. Find the length of time for which the ball is above 3 m from the point of projection.
7. A stone is dropped from the top of a cliff and a second later a second stone is thrown vertically downwards at 15 ms-1. Both stones reach the beach at the same time. How high is the cliff?
8. A ball is thrown vertically upwards at 25 ms-1 at the same time as another is thrown vertically downwards at 25 ms-1. How far apart are the balls after 2 seconds?
9. A bus sets off from stop A and accelerates uniformly for t1 seconds covering 300 m. It then travels at a constant speed v for t2 seconds covering another 1250 m. It decelerates for t3 seconds to come to rest at stop B. Given that the total time for the journey is 3 minutes and that 2t1 = 3t3, find t1, t2, t3, v, and the distance AB. (Hint: Use a method similar to Question 5.)
Name: AS Further Maths
As well as on VTE all files at:
HYPERLINK "http://tinyurl.com/furthermathsinduction" http://tinyurl.com/furthermathsinduction
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